You have to look at it from his pov here.
You're peeling down his clothes and whipping off his nappy in a cold house and he has no idea why. You've introduced a potty in the living room but he has absolutely no idea what he's supposed to do with it. It looks and feels like a seat that is just for him to sit on, which is a perfectly reasonable assumption. After all, he's never seen you sitting in it and using it for its intended purpose. He is also supposed to understand when he needs to pee and to tell you, so he can have his bottom bared in a cold room and sit on the cold and mysterious potty, when up to now he has peed whenever he felt like it or even without noticing it
Potty training requires a lot of ground work ahead of the final stretch (the part when you take the nappies away and DC start using the potty is the final stretch).
He should be going upstairs with you and watching you and his dad use the loo as much as possible. Every time would be great. He will be naturally curious about the magic that happens in the bathroom and will want to have a go too. It would help greatly if you could heat the bathroom.
Take a few weeks to introduce him to the loo, why people go there and what what people do there. Narrate every single time: say 'I feel I need to pee/ poop', do a little pee-pee dance, say 'I need to go up to the loo and pee/ poop there so I can keep my pants dry'. Narrate how people pull down their pants, sit on the loo, wait for the pee/ poop, make sure they're all finished, get up, wipe, pull up pants, flush, wash hands, dry hands. Let him flush like a big boy.
It's a good idea to have a little clip-on toilet seat handy in the bathroom, and a step stool, so he can easily have a go himself if he feels enthusiastic about having his own loo adventure.
When you get started, keep the potty in the kitchen where I assume there's no carpet. But you have to lay a lot of ground work before you start.
Edited to add - he has no preconceptions at all about the 'big potty' upstairs. Likewise, there is nothing obvious about the little downstairs potty that will make him understand what it's all about. I started all but my first DC on the big potty with the clip on seat, having graduates DC1 off the little potty when we forgot to bring it with us on a visit to gran's house.